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arXiv · 1106.3879

Dynamical elastic bodies in Newtonian gravity

Lars Andersson·Todd A. Oliynyk·Bernd G. Schmidt
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Abstract

Well-posedness for the initial value problem for a self-gravitating elastic body with free boundary in Newtonian gravity is proved. In the material frame, the Euler-Lagrange equation becomes, assuming suitable constitutive properties for the elastic material, a fully non-linear elliptic-hyperbolic system with boundary conditions of Neumann type. For systems of this type, the initial data must satisfy compatibility conditions in order to achieve regular solutions. Given a relaxed reference configuration and a sufficiently small Newton's constant, a neigborhood of initial data satisfying the compatibility conditions is constructed.

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Lars Andersson, Todd A. Oliynyk, Bernd G. Schmidt. 2011-06-20. Dynamical elastic bodies in Newtonian gravity. https://doi.org/10.1088/0264-9381%2F28%2F23%2F235006

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